Tricritical point of lattice QCD with Wilson quarks at finit

First principle study of QCD at finite temperature $T$ and chemical potential $\mu$ is essential for understanding a wide range of phenomena from heavy-ion collisions to cosmology and neutron stars. However, in the presence of finite density, the critical

4

002 voN 61 3v9105040/tal-ep:hviXraTricriticalpointoflatticeQCDwithWilsonquarksat nitetemperatureanddensity

Xiang-QianLuo

CCAST(WorldLaboratory),P.O.Box8730,Beijing100080,China

DepartmentofPhysics,Zhongshan(SunYat-Sen)University,Guangzhou510275,China

(February1,2008)FirstprinciplestudyofQCDat nitetemperatureTandchemicalpotentialµisessentialforunderstandingawiderangeofphenomenafromheavy-ioncollisionstocosmologyandneutronstars.However,inthepresenceof nitedensity,thecriticalbehaviorlatticegaugetheorywithoutspeciesdoubling,isunknown.Atstrongcoupling,weexaminethephasestructureonthe(µ,T)plane,usingHamiltonianlatticeQCDwithWilsonfermions.Atricriticalpointisfound,separatingthe rstandsecondorderchiralphasetransitions.Suchatricriticalpointat niteThasnotbeenfoundinpreviousworkintheHamiltonianformalismwithKogut-Susskindfermionsornaivefermions.12.38.Gc,11.10.Wx,11.15.Ha,12.38.Mh

PublishedinPhys.Rev.D70,091504(RapidCommun.)(2004).

I.INTRODUCTION

InLagrangianformulationofSU(3)LGTat niteµ,complexactionspoilsnumericalsimulationswithimpor-Oneofthemostchallengingissuesinparticlephysicstancesampling.TherecentyearshaveseenenormousistostudyQCDinextremeconditions.Precisedetermi-e orts[4–6]onsolvingthecomplexactionproblem,andnationoftheQCDphasediagramontemperatureTandsomeveryinterestinginformation[7]onthephasedia-chemicalpotentialµplanewillprovidevaluableinfor-gramforQCDwithKSfermionsatlargeTandsmallmationforquark-gluonplasma(QGP)andneutronstarµhasbeenobtained.Nevertheless,topreciselylocatephysics.

thetricriticalpointandcriticallineatlargeµisstillForQCDwithtwomasslessquarks,severalapproxi-anextremelydi culttask.Onehasalsotoresolvethemationmodels(e.g.linearsigmamodel,Nambu-Jona-contradictionbetweenMonteCarlo(MC)simulationsatLasinomodel,randommatrixmodel,statisticalboot-intermediatecouplingandstrongcouplinganalysisfor1strap)[1]suggesttheexistenceofatricriticalpointonstaggered avor(correspondingto4 avorsinthecontin-the(µ,T)planeseparatingthe rstordertransitionlineuum):MCdata[6]indicatethatthechiralphasetran-atlowerTandlargerµ,andthesecondordertransitionsitionatµ=0andsome niteTCisof rstorder,lineathigherTandsmallerµ.Therehasbeenapro-whilestrongcouplinganalysis[8,9]favorsthesecondor-posal[2]forexperimentalsearchforthetricriticalpoint,dertransition;TheauthorofRef.[9]studiesthephaseviaevent-by-event uctuationsinheavy-ioncollisions.diagramonthe(µ,T)plane,anddiscoversatricriticalLatticegaugetheory(LGT),proposedbyWilson[3]point,whileinMCsimulation[6],onlyalineof rstor-isthemostreliablenon-perturbativeapproachtoQCD,derphasetransitionisfound.Itmightwellbethattheybasedon rstprinciples.Unfortunately,itsu ersprob-belongtodi erentuniversalityclasses.

lemslikethecomplexactionat niteµandspeciesdou-QCDatlargeµisofparticularimportanceforneu-blingwithnaivefermions.

tronstarorquarkstarphysics.Hamiltonianformula-Kogut-Susskind(KS)’sapproachtolatticefermionstionofLGTdoesn’tencounterthenotorious“complexthinsthedegreesoffreedom,andpreservestheremnantactionproblem”.Recently,weproposedaHamiltonianofchiralsymmetry,butitdoesn’tcompletelysolvetheapproachtoLGTwithnaivefermionsat niteµ[10,11],speciesdoublingproblem;Itbreaksthe avorsymme-andextendedittoWilsonfermions[12].Thechiralphasetryaswell.Wilson’sapproachtolatticefermions[3]transitionatT=0andsome niteµCwasfoundtobehasbeenextensivelyusedinhadronspectrumcalcula-of rstorder.InRefs.[13,14],theauthorsstudiedthetionsaswellasinQCDat nitetemperature;ItavoidsphasediagramofQCDwithKSfermionsfor2and4 a-thespeciesdoublingandpreservesthe avorsymmetry,vorsandnaivefermionsfor4 avors.Alineofsecondbutitexplicitlybreaksthechiralsymmetry,oneoftheorderphasetransitionwasfoundinbothcases,butnomostimportantsymmetriesoftheoriginaltheory;Non-tricriticalpointwasfoundatany niteT.

perturbative ne-tuningofthebarefermionmasshastoInthispaper,westudythephasediagramusingHamil-bedone,inordertode nethechirallimit.

tonianlatticeQCDwithWilsonfermions.Atstrongcou-

First principle study of QCD at finite temperature $T$ and chemical potential $\mu$ is essential for understanding a wide range of phenomena from heavy-ion collisions to cosmology and neutron stars. However, in the presence of finite density, the critical

plingandinthenon-perturbativelyde nedchirallimit,we ndatricriticalpointonthe(µ,T)plane.Therestofthepaperisorganizedasfollows.InSec.II,wederivethee ectiveHamiltonianat niteTandµ.InSec.III,weanalyzetheQCDphasediagram.Theresultsaresum-marizedinSec.IV.

II.EFFECTIVEHAMILTONIANATTHE

STRONGCOUPLING

A.Theµ=0case

AccordingtoEq.(3)andfollowingtheprocedureinSec.IIA,theroleoftheHamiltonianatstrongcouplingisnowplayedby

µHeff=Heff µN.

(5)

ThevacuumenergyistheexpectationvalueofH µN

initsgroundstate| ,andalsotheexpectationvalueofµHeffinitsgroundstate| eff ,givenby

µ

E = |H µN| = eff|Heff| eff .

(6)

WebeginwithQCDHamiltonianwithWilson

fermionsatµ=0on1dimensionalcontinuumtimeandd=3dimensionalspatialdiscretizedlattice,

¯(x)ψ(x)H=Mψ

x

C.ResultsforlargeNc

+

1

d xj=1

AsshowninRef.[12],underthemean- eldapproxima-tion,i.e.,byWick-contractingapairoffermion eldsin

thefourfermiontermsinHeff,onecanobtainabilinearHamiltonianinleadingorderof1/Nc

µµ¯(x)ψ(x)ψHeff～HMFA=A

x

2a

1

αα

Ej(x)Ej(x)

+(B µ)

whereA=M

a4aNc

Kd

v

2

2

x

ψ (x)ψ(x)+C,

(7)

a

,(2)…… 此处隐藏：9330字，全部文档内容请下载后查看。喜欢就下载吧 ……